A glassware forming machine of the so-called "Individual Section" type normally has a blank station at which a parison is formed from a gob of molten glass and a blow station at which the parison is formed into an article of glassware. The parison formed at the blank station is transferred to the blow station to be blown. It has long been recognised that it is desirable to allow the parison to reheat before being moulded at the blow station. This reheating serves to allow portions of the parison which where in contact with a mould at the blank station and have therefore become chilled to be reheated by other parts of the parison transferring heat thereto. In a more recently proposed type of individual section machine, see U.K. Patent Specification No. 1599801, a reheating intermediate station is provided between the blank station and the blow station so that parisons can be allowed to reheat at the intermediate station without causing delay in the operation of the blow station. However, it has been found that parisons at the intermediate station are subject to being chilled by up drafts of cold air created by the cold air displacing air heated by the parison. The provision of a fixed screen beneath the parison to prevent such up drafts is not practical because of the possibility that the parisons may need to be dropped from the intermediate station in the event of a malfunction of the machine.